Question

A line segment has endpoints A(4, 8) and B(2, 10). The point M is the midpoint of AB. What is an equation of a line perpendicular to AB and passing through M?

Answer 1

i)

The Midpoint M of the line segment AB is found using the Midpoint formula:


`M=( (4+2)/(2) , (8+10)/(2))=(3, 9)`

ii)

the slope of the line through A and B is found by the slope formula:


`m= (y_1-y_2)/(x_2-x_1)= (10-8)/(2-4)= (2)/(-2)=-1`

iii)

the product of the slopes of 2 perpendicular lines is -1, so the slope of the line perpendicular to the line through A and B is -1/(-1)=1

iv)

the equation of the line with slope 1, which contains point M(3, 9) is found by the slope point form equation of a line:

y-9=1(x-3)

y-9=x-3

y=x+6


Answer: y=x+6